Stochastic Normalizing Flows for Inverse Problems: A Markov Chains Viewpoint

Paul B. Rohrbach, Sergey Dolgov, Lars Grasedyck, Robert Scheichl

Research output: Contribution to journalArticlepeer-review

1 Citation (SciVal)
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To overcome topological constraints and improve the expressiveness of normalizing ow architectures, Wu, Kohler, and Noe introduced stochastic normalizing ows which combine deterministic, learnable ow transformations with stochastic sampling methods. In this paper, we consider stochastic normalizing ows from a Markov chain point of view. In particular, we replace transition densities by general Markov kernels and establish proofs via Radon-Nikodym derivatives, which allows us to incorporate distributions without densities in a sound way. Further, we generalize the results for sampling from posterior distributions as required in inverse problems. The performance of the proposed conditional stochastic normalizing ow is demonstrated by numerical examples.

Original languageEnglish
Pages (from-to)1162-1190
Number of pages29
JournalSIAM/ASA Journal on Uncertainty Quantification
Issue number3
Early online date28 Sept 2022
Publication statusPublished - 30 Sept 2022


  • math.NA
  • cs.NA
  • math.ST
  • stat.TH
  • 15A23, 15A69, 65C60, 65D32, 65D15, 41A10
  • Markov chain Monte Carlo
  • inverse problems
  • invertible neural networks

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Modelling and Simulation


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